Answer
See below
Work Step by Step
The volume of the resulting pearl with radius $r$ is $\frac{4 \pi r^3}{3}$
Since a diameter of a bead is 6 millimeters, its radius is 3 millimeters, and its volume is $\frac{4\pi (3)^3}{3}$ millimeters cubed.
A diameter of a bead is 9 millimeters; its radius is 4.5 millimeters; and its volume is $\frac{4\pi (4.5)^3}{3}$ millimeters cubed.
The ratio of these two volumes is: $\frac{\frac{4\pi (4.5)^3}{3}}{\frac{4\pi (3)^3}{3}}=\frac{4.5^3}{3^3}=(\frac{4.5}{3})^3=1.5^3$
Simplify: $1.5^3=1.5\times1.5\times1.5=2.25\times1.5=3.375$
The volume of a pearl is $3.375$ greater than the volume of a bead.
